The 20-year-old played twice for the Netherlands in the recent UEFA European Under-21 Championships, after establishing himself in Utrecht's starting XI last season, making 31 appearances and scoring four times.
And the centre-back is hopeful he can continue his recent success with the Amsterdam club, after it secured a third straight Eredivisie title in 2013.
"I am very happy with this contract and am looking forward to starting training soon," he told the club's official website.
"I have only heard positive words about Ajax.
"Ajax have been champions for the last three seasons, so I hope that will continue in the next four years."
Van der Hoorn conceded it will be difficult to establish himself in the Ajax side, but is relishing the challenge of fighting for a starting spot.
"Ajax has a lot of competition in defence, but that's not a problem," he added.
"Competition only makes you better.
"In addition, I hope to learn a lot from [manager] Frank de Boer and [assistant] Jaap Stam, in their time they were the best defenders in the world."